expression_Add_Operator.java

/*

Given a string that contains only digits 0-9 and a target value, return all possibilities to add binary operators (not unary) +, -, or * between the digits so they evaluate to the target value.

Example 1:

Input: num = "123", target = 6
Output: ["1+2+3", "1*2*3"] 
Example 2:

Input: num = "232", target = 8
Output: ["2*3+2", "2+3*2"]
Example 3:

Input: num = "105", target = 5
Output: ["1*0+5","10-5"]
Example 4:

Input: num = "00", target = 0
Output: ["0+0", "0-0", "0*0"]
Example 5:

Input: num = "3456237490", target = 9191
Output: []
*/

class Solution {
    
    //Backtracking 
public List<String> addOperators(String num, int target) {
    List<String> res = new ArrayList<>();
   	StringBuilder sb = new StringBuilder();
    dfs(res, sb, num, 0, target, 0, 0);
    return res;
    
}
public void dfs(List<String> res, StringBuilder sb, String num, int pos, int target, long prev, long multi) { 
	if(pos == num.length()) {
		if(target == prev) res.add(sb.toString());
		return;
	}
	for(int i = pos; i < num.length(); i++) {
		if(num.charAt(pos) == '0' && i != pos) break;
		long curr = Long.parseLong(num.substring(pos, i + 1));
		int len = sb.length();
		if(pos == 0) {
			dfs(res, sb.append(curr), num, i + 1, target, curr, curr); 
			sb.setLength(len);
		} else {
			dfs(res, sb.append("+").append(curr), num, i + 1, target, prev + curr, curr); 
			sb.setLength(len);
			dfs(res, sb.append("-").append(curr), num, i + 1, target, prev - curr, -curr); 
			sb.setLength(len);
			dfs(res, sb.append("*").append(curr), num, i + 1, target, prev - multi + multi * curr, multi * curr); 
			sb.setLength(len);
		}
	}
}
}